Squaring Function Squaring Function Zehavit Trachtenberg Ido Dinerman Barak Cohen.
Squaring rounding method
11
Extra Math: Methods, Tips And Tricks Series. By Puwork Utara May 2012
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Transcript of Squaring rounding method
Extra Math:
Methods, Tips And Tricks Series.
By Puwork UtaraMay 2012
ROUNDING SQUARING
40 41 42 43 44 45 46 47 48 49 50
45 is 3 more than 42 but 3 less than 48,
+ 3- 3
or, 45 – 3 = 42 and comparatively, 45 + 3 = 48
Foreword
Calculation using Rounding Method, Illustration 2 is more useful and practical.You can see “why” on next slides…
40 41 42 43 44 45 46 47 48 49 50
45 is 5 more than 40 but 5 less than 50,
+ 5- 5
or, 45 – 5 = 40 and, comparatively, 45 + 5 = 50
Illustration 1
Illustration 2
Compare the Illustration 1 and Illustration 2..
45 X 45Example 1:
40 41 42 43 44 45 46 47 48 49 50
+ 5- 5
45 2
40
50
- 5
+ 5
( 40 X 50 ) + 5 = 2025 2
How to Square
45 2 = ( 40 X 50 ) + 5 2
= 2000 + 25
= 2025
Briefly..
Figure out…. Where is 45..to be rounded
Simplified
45..is nearest to either 40 or 50
73 X 73Example 2:
70 71 72 73 74 75 76 77 78 79 70
+ 3- 3
73 2
70
76
- 3
+ 3
( 70 X 76 ) + 3 = 5329 2
How to Square
73 2 = ( 70 X 76 ) + 3 2
= 5320 + 09
= 5329
Briefly..
Figure out…. Where is 73...
Simplified
In this case, 73..is nearest to 70.
58 X 58Example 3:
58 2
60
56
+ 2
- 2
( 60 X 56 ) + 2 = 3364 2
In Diagrammed Solution
582 = ( 60 X 56 ) + 2 2
= 3360 + 04
= 3364
Where is 58..?.
Simplified Solution
Yep! 58..is nearest to 60.
105 X 105Example 4:
Where is 105..?.
Yep! 105..is 5 away from 100
105 2
100
110
- 5
+ 5
( 100 x 110 ) + 5 2 = 11025
Diagrammatically
=105 2 ( 100 x 110 ) + 5 2
= 11000 + 25
= 11025
Simplified
428 X 428Example 5:
4282
400
456
- 28
+28
( 400 x 456 ) + 28 = 182400 + 784 2
Diagrammatically
4282 = ( 400 x 456 ) + 28 2
= 182400 + 784
= 183184
Simplified Solution
Yep! 428..is nearest to 400, or 428 is (-28) away from 400
28 2
20
36
- 8
+8
( 20 X 36) + 8 = 784 2
Why this tricks work out ?
= 40(50) - 40(5) + 5(50) - 5(5)
An example to be deduced.
45 = 40 + 5 and also 45 = 50 - 5
So, 45 X 45 = ( 40 + 5 )( 50 – 5 )
= 40(50) + 5(50) - 40(5) - 5(5) Rearranged
Refactorised= 40(50) + 5( 50 - 40 - 5 )
= 40(50) + 5( 5 ) Simplified
= 2000 + 25
= 2025 Final Answer
But why this tricks work out ?
40 41 42 43 44 45 46 47 48 49 50
+ 5- 5
To figure out
Expanded
GOOD LUCK !
End Show
Thanks!
